Abstract

Non-steady behavior of a flame stabilized in a two-dimensional duct is studied in this thesis. The problem is formulated by an integral technique in which the governing equations are integrated across the duct to obtain integral relations for the mean flow variables. The flow fields on either side of the flame sheet are matched by appropriate matching conditions. Fluid flow through the flame surface causes the integral relations to explicitly involve the fluid velocities at the flame. An independent description of the flame shape and the irrotational flow field upstream of the flame is provided by a source distribution on the duct axis.

The integral relations are analyzed by a perturbation technique, in which the dominant order solution represents the steady flame development. The steady flame configuration is perturbed by an acoustic wave incident on the compact flame region. The time dependent counterpart of the integral relations describes the ensuing non-steady flow fields. The flame perturbation exhibits a travelling wave pattern with considerable amplification along the flame zone. A simple model to describe the growth of the flame perturbation is put forth, by considering the flame surface as an unstable shear layer.

Acoustic reflection and transmission coefficients of the flame region are obtained utilizing the time-dependent flame calculations. The response spectra exhibit active responses at certain well defined frequencies. The non-steady flame model is incorporated in a rudimentary afterburner configuration to investigate the low frequency behaviour of the afterburner. The results suggest a possible mechanism of low frequency instability in a combustion system.